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Weak reciprocal continuity and fixed point theorems. (English) Zbl 1223.54068

Authors’ abstract: The aim of the present paper is to introduce the notion of weak reciprocal continuity and obtain fixed point theorems by employing the new notion. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. Our results generalize several fixed point theorems.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54E40 Special maps on metric spaces
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